How many laps will Matt run in 16 minutes using the linear equation

Compound Interest

The final value of an investment of P dollars for t years at an interest rate of r is given by:

Where m is the number of compounding periods per year.

(a)

Lori buys a CD for P = $1500 that earns r = 6% = 0.06 interest compounded monthly for t = 10 years. Here m = 12 because there are 12 months in a year.

Substituting:

The CD will be worth $2729.10 in 10 years.

(b) If the interest compounds daily, then m = 360. Calculating:

The CD will be worth $2733.04 in 10 years.

(c) For t = 5 years:

The CD will be worth $2024.74 in 5 years.

The vector DC in terms of p is 2/3p and vector BC in terms of p and q is q + 1/2p

Given that,

ABCD is a trapezium.

AB  = p

AD = q

An identical one pair of opposite sides that are parallel to one another make up a trapezium, which is a convex quadrilateral. When represented as a table on a piece of paper, the trapezium is a two-dimensional shape. A polygon with four sides and four vertices is referred to as a quadrilateral in Euclidean geometry. Because of this, a trapezium also has four vertices, four angles, and four sides.

To find : The vector DC in terms of p  and vector BC in terms of p and q.

a) DC /AB = 3/2 ⇒

DC = 3/2AB = 3/2p

b) BC =AD + (dC - AB)

BC = q+(3/2p-p)= q+1/2p

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The value of the double integral is zero.

To evaluate the double integral, we need to convert the Cartesian coordinates to polar coordinates since the region is a circle. Let's recall the formula for changing variables in double integrals:

\($\iint_R f(x,y) dA = \iint_S f(r\cos\theta, r\sin\theta) r dr d\theta$\)

where\($R$\) is the region in the \($xy$\)-plane and\($S$\) is the region in the \(r\theta$-\)plane.

In this case, the region \($D$\) is a circle with center at the origin and radius \($4$\), so we have:

\($\iint_D (6x-2y) dA = \int_0^{2\pi} \int_0^4 (6r\cos\theta - 2r\sin\theta) r dr d\theta$\)

\($= \int_0^{2\pi} \int_0^4 (6r^2\cos\theta - 2r^2\sin\theta) dr d\theta$\)

\($= \int_0^{2\pi} \left[3r^3\cos\theta - r^3\sin\theta\right]_0^4 d\theta$\)

\($= \int_0^{2\pi} (48\cos\theta - 64\sin\theta) d\theta$\)

\($= \left[48\sin\theta + 64\cos\theta\right]_0^{2\pi}$\)

\($= 0$\)

Therefore, the value of the double integral is zero.

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(complete question)

evaluate the double integral. (6x-2y)dA D is bounded by the circle with the center at the origin and radius 4. What to evaluate the integral for x and y.

Answer:

im not sure about this, but ithink i know how to solve it!

Step-by-step explanation:

you have to take the 10and multiply its self by 70 (10 x 10 x 10 x 10 x10 x 10 x10)

and then take what you got by multiplying that, and multipy by 4.457. then you do they same for the other two, then add them all together :)

It would take 5040 cubic inches of water to completely fill the aquarium.

We know that the formula for the volume of cuboid :

V = length × width × height

Let us assume that l represents the length of the aquarium, w represent the width and h represents the height.

Here, l = 20 inches

w = 14 inches

and h = 18 inches

Using the formula for the volume of cuboid, the volume of aquarium would be,

V = l × w × h

V = 20 × 14 × 18

V = 5040 cu.in.

Therefore, it would take 5040 cu.in. of water.

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The critical value of f(x) = 5x⁶ - 3x⁵ is x = 0.5 which is also its maxima point

f(x) = 5x⁶ - 3x⁵

differentiation w.r.t x

=> f'(x) = 30x⁵ - 15x⁴

Putting f'(x) = 0

30x⁵ - 15x⁴ = 0

=> x⁴(30x - 15) =0

=> 30x - 15 = 0

=> x = 15/30

=> x = 0.5 , 0

Critical number is 0.5 , 0

(B) To find where f(x) is increasing

for x > 0.5 ,

(30x-15) > 0 => x⁴(30x - 15) > 0

Therefore , f(x) is increasing at ( 0.5 , ∞ )

(C)To find where f(x) is decreasing

for x < 0.5 ,

(30x-15) < 0 => x⁴(30x - 15) < 0

Therefore , f(x) is decreasing at ( -∞ , 0.5)

(D) Differentiation f'(x) again w.r.t to x

f'(x) = 30x⁵ - 15x⁴

f"(X) = 150x⁴ - 60x³

Substituting critical values of x

=> 150(0.5)⁴ - 60(0.5)³

=>9.375 - 7.5

=> -1.875 < 0 , Hence , x = 0.5 is point of maxima

(E) no point of minima

Similarly , we can solve other parts

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The length of the apothem is equal to 7.46in

Data;

This can be calculated using the formula

\(A = \frac{s}{2*tan(\frac{180}{n}) } \\A = \frac{4}{2*tan(\frac{180}{12}) } \\A = 7.46in\)

The length of the apothem is equal to 7.46in

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Answer:

1296

Step-by-step explanation:

6x6x6x6

6^4

Answer:

6×6×6×6

Step-by-step explanation:

I hope this helps

Answer: 3 1/2

Step-by-step explanation:

If this isn’t right then let me know but I think it is

Answer:

(-1,0)

Step-by-step explanation:

Answer:

150 total eggs cracked

Step-by-step explanation:

I don't know how others do it but this is my way (fast and easy)

1,350/18

= 75

75*2

=150 total eggs cracked

Answer:

150 eggs expect to be cracked if there are a total of 1,350 in the grocery store.

Step-by-step explanation:

18 eggs - 2 cracked  = 16 eggs were good condition at  grocery story

1,350 eggs  / 18 eggs = 75

75 x 2 = 150

1,350 - 150 = 1200

Out of 1350 eggs,  1200 eggs  were good condition at  grocery story

150 eggs expect to be cracked if there are a total of 1,350 in the grocery store.

The amount of money that Jason will receive in one year after all deductions have been taken for each company is $30,780.5 and $32562.

With the first job, he would be an apartment property manager for AMLI Company.

This job is offering Jason an hourly rate of $19. 00 an hour plus a weekly bonus of $40 for each new tenant he sets a one-year lease-up with.

The company expects Jason to work all 52 weeks of the year and 40 hours per week.

He was told he could expect to set up an average of 5 lease agreements for each week that he works.

The amount after one year will be given by an equation

Let y be the amount, x be the number of hours in a week and z be the number of the week.

y = 19x + 40z

The total number of hours in a year will be

x = 2080

Then

y = 19 × 2080 + 40 × 52

y = $ 41,600

The amount after the deduction of Social Security (6. 2%), Medicare (1. 2%), State Income Tax (3%), and Federal Income Tax (14%) will be

→ 41,600 × 0.938 × 0.988 × 0.97 × 0.86

→ $ 32,160.5

The amount after the insurance will be

Amount = 32160.5 - 115 × 12

Amount = $ 30780.5

With the second job, he would work as a water treatment facility manager in Gwinnett County. He would be paid an annual salary of $46,000 a year, there are no bonuses and he gets a week off.

The amount after the deduction of Social Security (6. 2%), Medicare (1. 2%), State Income Tax (3%), and Federal Income Tax (14%) will be

→ 46,000 × 0.938 × 0.988 × 0.97 × 0.86

→ $ 35,562

The amount after the insurance will be

Let the number of the worker be 10. Then

Amount = 35,562 - 10 × 12 × 25

Amount = 35562 - 3000

Amount = $32562

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Answer:

0.9

Step-by-step explanation:

In order to get halfway between -0.5 and 2.3, first, we need to take their sum:

Sum of digits

Sum =  \({-0.5+2.3}\)

Sum =  \(1.8\)

Take the average of the sum

Average = \(\frac{1.8}{2} = 0.9\)

Hence the halfway between the numbers is 0.9

Answer:

27

Step-by-step explanation:

Answer:

ST=27   (Hope this helps)

Step-by-step explanation:

         RS+ST=100

           2x+7+x-6=100

             3x+1=100

               3x=99

                 x=33

         ST=33-6

           ST=27

Answer:

A

Step-by-step explanation:

Answer:

x = 12

Step-by-step explanation:

8x-4 = 92

Corresponding Angle

8x = 92+4

8x = 96

Divide by 8

x = 12

Answer: 10,000

Step-by-step explanation:Hope this helps!

Answer:

  (x, y) = (1, 1)

Step-by-step explanation:

A graphing calculator works nicely for solving equations graphically.

__

If you want to plot these by hand, it is convenient to write them in slope-intercept form:

  y = -2x +3 . . . . . subtract 2x from both sides of the first equation

  y = x . . . . . . . . . add y to both sides of the second equation

These tell you the first line goes through (0, 3) with a slope of -2. The second line goes through the origin with a slope of +1.

The solution is ...

  (x, y) = (1, 1)

_____

Additional comment

Slope-intercept form is not the only convenient form for graphing the equation of a line. The first equation, for example, is given in standard form, which makes it easy to see the x-intercept is 3/2, and the y-intercept is 3. Sometimes plotting points with a fractional coordinate can be problematical, so we choose to put that equation into a different form.

The second equation quite clearly tells us y=x, so we know that line goes through points that have the same x- and y-coordinates.

The standard error of the mean for a simple random sample of 100 observations, with a sample mean of 80 and a standard deviation of 12, is 1.20 (option a).

The standard error of the mean measures the precision or variability of the sample mean estimate. It is calculated by dividing the standard deviation of the population by the square root of the sample size.

Given that the sample mean is 80 and the standard deviation is 12, we can calculate the standard error of the mean as follows:

Standard Error of the Mean = Standard Deviation / Square Root of Sample Size

Standard Error of the Mean = 12 / √100 = 12 / 10 = 1.20

Therefore, the standard error of the mean for this sample is 1.20. This value indicates the average amount of variability or uncertainty we can expect in the sample mean compared to the population mean. It represents the precision of the sample mean estimate and is an important measure in inferential statistics for making inferences about the population based on the sample.

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Answer:

x = - 1/2

Step-by-step explanation:

x - 2 = 3x - 1    We have to subtract x from both sides of the equation and we    have to add 1 to both sides of the equation.

-1 = 2x           Divide 2 from both sides of the equation

x = - 1/2           <-- This is your answer

Hope this helps!

Using the z table, the critical value \(z_{a/2}\) needed to construct a confidence interval with level 82% is 1.34.

In the given question,

We have to find the critical value \(z_{a/2}\) needed to construct a confidence interval with level 82%.

The confidence interval is 82%.

We can write 82% as 82/100 and 0.82.

Now the value of

\(\alpha\)=1−0.82

\(\alpha\)=0.18

Now finding the value of \(\alpha\)/2

\(\alpha\)/2=0.18/2

\(\alpha\)/2=0.09

Now finding the value of \(z_{a/2}\).

\(z_{0.82}\) = 1.34

Hence, the critical value \(z_{a/2}\) needed to construct a confidence interval with level 82% is 1.34.

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Answer:

Negative

Step-by-step explanation:

When you multiply a negative number by a positive number then the product is always negative.

Answer:

A width of 3 and a length of 9

Step-by-step explanation:

To solve this problem, we're going to have to create an equation. So, let's call the width w. The length of the rectangle is three times the width, so the length will be 3w. The total area is 27, and the length times the width must equal the area, so this gives us the following equation:

w(3w) = 27

Let's simplify and start solving.

3w² = 27

3w²/3 = 27/3

w² = 9

√w² = √9

w = 3

Remember, we defined w as the width. So, the width of the rectangle is 3. The length is 3w, or three times the width, so the length must be 9. And these are our dimensions: 3 × 9.

Answer:

26.7pounds

Step-by-step explanation:

Suppose that an individual has a body fat percentage of 15.9% in weighs 168 pounds

This is calculated as:

Pounds of his weight that is made up of fat is calculated as

Body fat percentage × Body weight in pounds

= 15.9% × 168 pounds

= 15.9/100 = 168 pounds

= 26.712 pounds

Approximately to the nearest tenth = 26.7 pounds

The congruent angles, ∠ACD and ∠BCD formed by the angle bisector \(\overline{DC}\) the congruent segments \(\overline{AC}\) and \(\overline{BC}\), and the segment \(\overline{DC}\) (congruent to itself, indicates that ΔACD ≅ ΔBCD by SAS

The SAS (Acronym for Side-Angle-Side) congruency rule states that two triangles, A and B are congruent if two sides and an included angle of the triangle A are congruent to the two sides and an included angle of the other triangle B.

The specified information are;

The bisector of ∠ACB = \(\overline{DC}\)

Segment \(\overline{AC}\) ≅ \(\overline{BC}\)

Required; to prove that ΔACD ≅ ΔBCD

The two-column method can be used to prove the congruency of the triangles as follows;

Step     \({}\)             Statement            \({}\)        Reasons

1.  \({}\)                    \(\overline{DC}\) bisects ∠ACB          Given

                 \({}\)      \(\overline{AC}\) ≅ \(\overline{BC}\)

2.  \({}\)                  ∠ACD ≅ ∠BCD              Definition of bisected angles

3.                \({}\)    \(\overline{CD}\) ≅ \(\overline{CD}\)                       Reflexive property of congruency

4. \({}\)                   ΔACD ≅ ΔBCD               SAS congruency rule

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Answer:sum of supplementary

measure=180°

a. Probability that exactly 25 of them survive their first year of lifeLet X be the number of bald eagles that survive their first year of life. Since there are only two possible outcomes (surviving or not surviving), X has a binomial distribution with parameters n = 41 and p = 0.63, which can be denoted by X ~ B (41, 0.63).P (X = 25) = 41C25 (0.63)25(0.37)16 ≈ 0.0388Therefore, the probability that exactly 25 bald eagles survive their first year of life is 0.0388.  

b. Probability that at most 28 of them survive their first year of lifeTo find this probability, we need to add the probabilities of the events in which X is less than or equal to 28. Using a binomial probability table, we can add the probabilities of P (X = 0), P (X = 1), ..., P (X = 28), which is:P (X ≤ 28) ≈ P (X = 0) + P (X = 1) + ... + P (X = 28)≈ 6.79 x 10^-15 + 1.20 x 10^-12 + ... + 0.2316+ 0.2969+ 0.3436+ 0.3697+ 0.3845+ 0.3943+ 0.3998+ 0.4019≈ 0.9651Therefore, the probability that at most 28 bald eagles survive their first year of life is 0.9651.

c. Probability that at least 27 of them survive their first year of lifeUsing the complement rule, we can find the probability that at least 27 bald eagles survive their first year of life:P (X ≥ 27) = 1 - P (X < 27) ≈ 1 - P (X ≤ 26)≈ 1 - 0.8852≈ 0.1148Therefore, the probability that at least 27 bald eagles survive their first year of life is 0.1148.  

d. Probability that between 23 and 31 (including 23 and 31) of them survive their first year of lifeUsing the cumulative probability function, we can find the probability that between 23 and 31 (inclusive) bald eagles survive their first year of life:P (23 ≤ X ≤ 31) ≈ P (X ≤ 31) - P (X < 23)≈ 0.9981 - 0.0182≈ 0.9799Therefore, the probability that between 23 and 31 bald eagles survive their first year of life is 0.9799.

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Answer: 1/3

Step-by-step explanation: so there is six cards total and only two of them are even so 2/6 and that can go to 1/3

1/3

There are 2 even numbers, and the total is 6. So 2/6 in the simplest form is 1/3.

Answer:

Step-by-step explanation:

The given triangle is a right angled triangle.

So, the angles in the triangle are :

Solving according to angle sum property,

Sum of all angles in a triangle is 180°

\(\longrightarrow\) 90° + (4x + 10)° + (2x + 26)° = 180°

\(\longrightarrow\) 126° + 6x = 180°

\(\longrightarrow\) 6x = 180° - 126°

\(\longrightarrow\) 6x = 54°

\(\longrightarrow\) x = 9

Angles =

\(\longrightarrow\) 4(9) + 10

\(\longrightarrow\) 46°

\(\longrightarrow\) 2(9) + 26

\(\longrightarrow\) 44°

The angles are 46°, 90° and 44°.